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Concurrency bugs are hard to discover and reproduce, even in well-synchronized programs that are free of data races. Thankfully, prior work on controlled concurrency testing (CCT) has developed sophisticated algorithms---such as partial-order based and selectively uniform sampling---to effectively search over the space of thread interleavings. Unfortunately, in practice, these techniques cannot easily be applied to real-world Java programs due to the difficulties of controlling concurrency in the presence of the managed runtime and complex synchronization primitives. So, mature Java projects that make heavy use of concurrency still rely on naive repeated stress testing in a loop. In this paper, we take a first-principles approach for elucidating the requirements and design space to enable CCT on arbitrary real-world JVM applications. We identify practical challenges with classical design choices described in prior work---such as concurrency mocking, VM hacking, and OS-level scheduling---that affect bug-finding effectiveness and/or the scope of target applications that can be easily supported. Based on these insights, we present Fray, a new platform for performing push-button concurrency testing (beyond data races) of JVM programs. The key design principle behind Fray is to orchestrate thread interleavings without replacing existing concurrency primitives, using a concurrency control mechanism called shadow locking for faithfully expressing the set of all possible program behaviors. With full concurrency control, Fray can test applications using a number of search algorithms from a simple random walk to sophisticated techniques like PCT, POS, and SURW. In an empirical evaluation on 53 benchmark programs with known bugs (SCTBench and JaConTeBe), Fray with random walk finds 70% more bugs than JPF and 77% more bugs than RR's chaos mode. We also demonstrate Fray's push-button applicability on 2,664 tests from Apache Kafka, Lucene, and Google Guava. In these mature projects, Fray successfully discovered 18 real-world concurrency bugs that can cause 371 of the existing tests to fail under specific interleavings. We believe that Fray serves as a bridge between classical academic research and industrial practice--- empowering developers with advanced concurrency testing algorithms that demonstrably uncover more bugs, while simultaneously providing researchers a platform for large-scale evaluation of search techniques.